pairwise co-prime and m mmm Then f(x) = 0 (m) has a solution if each of the congruences f(x) = 0 (m.) has a solution. Moreover, if s(m) denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), respec
pairwise co-prime and m mmm Then f(x) = 0 (m) has a solution if each of the congruences f(x) = 0 (m.) has a solution. Moreover, if s(m) denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), respec
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Corollary 4.3. Let f(x) € Zr] and {mma} be positive integers such that they are
pairwise co-prime and m = mmm. Then f(1) = 0 (m) has a solution if and only
if each of the congruences f(x) = 0 (m.) has a solution. Moreover, if s(m) and s(m.)
denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), respectively. Then
s(m) = s(m₁)s(m₂)...s(m.).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95695f99-d391-4910-9fb8-e458ff0dfbe3%2F24301e40-856f-4050-b09a-a267e5f01c4c%2Ffa15yo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Corollary 4.3. Let f(x) € Zr] and {mma} be positive integers such that they are
pairwise co-prime and m = mmm. Then f(1) = 0 (m) has a solution if and only
if each of the congruences f(x) = 0 (m.) has a solution. Moreover, if s(m) and s(m.)
denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), respectively. Then
s(m) = s(m₁)s(m₂)...s(m.).
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